Loosely-self-stabilizing Byzantine-tolerant Binary Consensus for Signature-free Message-passing Systems

Many distributed applications, such as cloud computing, service replication, load balancing, and distributed ledgers, e.g., Blockchain, require the system to solve consensus in which all nodes reliably agree on a single value. Binary consensus, where the set of values that can be proposed is either zero or one, is a fundamental building block for other “flavors” of consensus, e.g., multivalued, or vector, and of total order broadcast. At PODC 2014, Mostéfaoui, Moumen, and Raynal, in short MMR, presented a randomized signature-free asynchronous binary consensus algorithm. They demonstrated that their solution can deal with up to t Byzantine nodes, where t < n/3 and n is the number of nodes. MMR assumes the availability of a common coin service and fair scheduling of message arrivals, which does not depend on the current coin values. It terminates within O(1) expected time. Our study, which focuses on binary consensus, aims at the design of an even more robust consensus protocol. We do so by augmenting MMR with self-stabilization, a powerful notion of fault-tolerance. In addition to tolerating node and communication failures, self-stabilizing systems can automatically recover after the occurrence of arbitrary transient-faults; these faults represent any violation of the assumptions on which the system was designed to operate (provided that the algorithm code remains intact). We present the first loosely-self-stabilizing fault-tolerant asynchronous solution to binary consensus in Byzantine message-passing systems. This is achieved via an instructive transformation of MMR to a self-stabilizing solution that can violate safety requirements with the probability Pr = O(2−M ), where M ∈ Z+ is a predefined constant that can be set to any positive value at the cost of 3Mn + logM bits of local memory. The obtained self-stabilizing version of the MMR algorithm considers a far broader fault-model since it recovers from transient faults. Additionally, the algorithm preserves the MMR’s properties of optimal resilience and termination, i.e., t < n/3, and O(1) expected decision time. Furthermore, it only requires a bounded amount of memory.